Constraining Continuous Wiener Processes. Dirichlet studied the first boundary value problem, for the Laplace equation, proving the uniqueness of the solution and this type of problem in the theory of partial differential equations (PDEs).
This was later named the Dirichlet problem after him ([1]}).
Problems expressed within this framework were studied as early as 1840 by C.F. Gauss, and then by [2]}.
[3]} formulated a means for constraining Markov processes.
[4]} expanded upon previous research on barriers, which included boundary behavior of constrained Wiener processes between reflecting and repellent barriers.
[5]} derived the time taken to reach the maximum for a variety of constrained Wiener processes.
[6]} examined the constraining of Wiener processes via impulse control.
[7]} added necessary and sufficient conditions for the stability of such constrained processes.
The same authors studied large deviations for various metrics of reflecting Wiener processes under constraining ([8]}).
[9]} constrained the jumps of Backward SDEs.
